Analysis of xx-mith-te3-00041881-base.sdk
Contents
Original Sudoku
level: hard
position: 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. initial
Autosolve
position: 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 4,8 => CTR => A3: 6,9 * CNT 1 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 4,8 => CTR => A3: 6,9 * STA A3: 6,9 * CNT 1 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:07.595619
The following important HDP chains were detected:
* DIS # E2: 4,8 # B3: 3,7 => CTR => B3: 6,8,9 * PRF # E2: 4,8 + B3: 6,8,9 # E3: 3,7 => SOL * STA # E2: 4,8 + B3: 6,8,9 + E3: 3,7 * CNT 2 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. | initial |
| 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. | autosolve |
| 12..56....5.1.92.6..............8.61..1.6.82...8.219.53..6.....74.89......5....9. | pair_reduction |
| 123456789457189236986237154294578361531964827678321945319642578742895613865713492 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A2: 4,8 G3: 1,5 H3: 1,5 A6: 4,6 D4: 5,9 D5: 5,9 C7: 2,9 C8: 2,6 I8: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G3,H3: 1.. / G3 = 1 => 7 pairs (_) / H3 = 1 => 10 pairs (_) B7,B9: 1.. / B7 = 1 => 11 pairs (_) / B9 = 1 => 10 pairs (_) E7,E9: 1.. / E7 = 1 => 10 pairs (_) / E9 = 1 => 11 pairs (_) G8,H8: 1.. / G8 = 1 => 10 pairs (_) / H8 = 1 => 7 pairs (_) B7,E7: 1.. / B7 = 1 => 11 pairs (_) / E7 = 1 => 10 pairs (_) B9,E9: 1.. / B9 = 1 => 10 pairs (_) / E9 = 1 => 11 pairs (_) G3,G8: 1.. / G3 = 1 => 7 pairs (_) / G8 = 1 => 10 pairs (_) H3,H8: 1.. / H3 = 1 => 10 pairs (_) / H8 = 1 => 7 pairs (_) D3,F3: 2.. / D3 = 2 => 9 pairs (_) / F3 = 2 => 12 pairs (_) A4,C4: 2.. / A4 = 2 => 9 pairs (_) / C4 = 2 => 12 pairs (_) A4,A9: 2.. / A4 = 2 => 9 pairs (_) / A9 = 2 => 12 pairs (_) D3,D9: 2.. / D3 = 2 => 9 pairs (_) / D9 = 2 => 12 pairs (_) G3,H3: 5.. / G3 = 5 => 10 pairs (_) / H3 = 5 => 7 pairs (_) A4,A5: 5.. / A4 = 5 => 12 pairs (_) / A5 = 5 => 8 pairs (_) D4,D5: 5.. / D4 = 5 => 8 pairs (_) / D5 = 5 => 12 pairs (_) F7,F8: 5.. / F7 = 5 => 15 pairs (_) / F8 = 5 => 10 pairs (_) A4,D4: 5.. / A4 = 5 => 12 pairs (_) / D4 = 5 => 8 pairs (_) A5,D5: 5.. / A5 = 5 => 8 pairs (_) / D5 = 5 => 12 pairs (_) A6,B6: 6.. / A6 = 6 => 13 pairs (_) / B6 = 6 => 14 pairs (_) G8,G9: 6.. / G8 = 6 => 11 pairs (_) / G9 = 6 => 10 pairs (_) C8,G8: 6.. / C8 = 6 => 10 pairs (_) / G8 = 6 => 11 pairs (_) C3,C8: 6.. / C3 = 6 => 11 pairs (_) / C8 = 6 => 10 pairs (_) E2,E3: 8.. / E2 = 8 => 13 pairs (_) / E3 = 8 => 10 pairs (_) H1,I1: 8.. / H1 = 8 => 9 pairs (_) / I1 = 8 => 0 pairs (X) A2,E2: 8.. / A2 = 8 => 10 pairs (_) / E2 = 8 => 13 pairs (_) H1,H7: 8.. / H1 = 8 => 9 pairs (_) / H7 = 8 => 0 pairs (X) I1,I3: 9.. / I1 = 9 => 9 pairs (_) / I3 = 9 => 0 pairs (X) D4,D5: 9.. / D4 = 9 => 12 pairs (_) / D5 = 9 => 8 pairs (_) B7,C7: 9.. / B7 = 9 => 0 pairs (X) / C7 = 9 => 9 pairs (_) C1,I1: 9.. / C1 = 9 => 0 pairs (X) / I1 = 9 => 9 pairs (_) * DURATION: 0:00:08.651891 START: 13:53:00.478368 END: 13:53:09.130259 2025-04-04 * CP COUNT: (30) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:07.438252 START: 13:53:19.674690 END: 13:53:27.112942 2025-04-04 * SOLUTION FOUND * SAVE PR GRAPH xx-mith-te3-00041881-base-pr-002.dot * REASONING * DIS # E2: 4,8 # B3: 3,7 => CTR => B3: 6,8,9 * PRF # E2: 4,8 + B3: 6,8,9 # E3: 3,7 => SOL * STA # E2: 4,8 + B3: 6,8,9 + E3: 3,7 * CNT 2 HDP CHAINS / 30 HYP OPENED
Header Info
rating: 8685; r2: 290733; index: 41881
Solution
position: 123456789457189236986237154294578361531964827678321945319642578742895613865713492 solved
See section Deep Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* DIS # A3: 4,8 => CTR => A3: 6,9 * INC # A3: 6,9 => UNS * INC # E2: 4,8 => UNS * INC # E2: 3,7 => UNS * INC # G8: 1,5 => UNS * INC # G8: 3,6 => UNS * INC # H8: 1,5 => UNS * INC # H8: 3 => UNS * INC # A3: 4,6 => UNS * INC # A3: 8,9 => UNS * INC # A4: 5,9 => UNS * INC # A4: 2,4 => UNS * INC # A5: 5,9 => UNS * INC # A5: 4 => UNS * INC # C4: 2,9 => UNS * INC # C4: 3,4,7 => UNS * INC # A9: 2,6 => UNS * INC # A9: 8 => UNS * INC # I9: 2,3 => UNS * INC # I9: 4,7,8 => UNS * INC # F8: 2,3 => UNS * INC # F8: 5 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 4,8 => CTR => A3: 6,9 * INC A3: 6,9 # E2: 4,8 => UNS * INC A3: 6,9 # E2: 3,7 => UNS * INC A3: 6,9 # G8: 1,5 => UNS * INC A3: 6,9 # G8: 3,6 => UNS * INC A3: 6,9 # H8: 1,5 => UNS * INC A3: 6,9 # H8: 3 => UNS * INC A3: 6,9 # A4: 5,9 => UNS * INC A3: 6,9 # A4: 2,4 => UNS * INC A3: 6,9 # A5: 5,9 => UNS * INC A3: 6,9 # A5: 4 => UNS * INC A3: 6,9 # C4: 2,9 => UNS * INC A3: 6,9 # C4: 3,4,7 => UNS * INC A3: 6,9 # A9: 2,6 => UNS * INC A3: 6,9 # A9: 8 => UNS * INC A3: 6,9 # I9: 2,3 => UNS * INC A3: 6,9 # I9: 4,7,8 => UNS * INC A3: 6,9 # F8: 2,3 => UNS * INC A3: 6,9 # F8: 5 => UNS * INC A3: 6,9 # E2: 4,8 => UNS * INC A3: 6,9 # E2: 3,7 => UNS * INC A3: 6,9 # B3: 6,9 => UNS * INC A3: 6,9 # C3: 6,9 => UNS * INC A3: 6,9 # G8: 1,5 => UNS * INC A3: 6,9 # G8: 3,6 => UNS * INC A3: 6,9 # H8: 1,5 => UNS * INC A3: 6,9 # H8: 3 => UNS * INC A3: 6,9 # A4: 5,9 => UNS * INC A3: 6,9 # A4: 2,4 => UNS * INC A3: 6,9 # A5: 5,9 => UNS * INC A3: 6,9 # A5: 4 => UNS * INC A3: 6,9 # C4: 2,9 => UNS * INC A3: 6,9 # C4: 3,4,7 => UNS * INC A3: 6,9 # A9: 2,6 => UNS * INC A3: 6,9 # A9: 8 => UNS * INC A3: 6,9 # I9: 2,3 => UNS * INC A3: 6,9 # I9: 4,7,8 => UNS * INC A3: 6,9 # F8: 2,3 => UNS * INC A3: 6,9 # F8: 5 => UNS * STA A3: 6,9 * CNT 39 HDP CHAINS / 39 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 4,8 => UNS * INC # E2: 3,7 => UNS * INC # B3: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # G8: 1,5 => UNS * INC # G8: 3,6 => UNS * INC # H8: 1,5 => UNS * INC # H8: 3 => UNS * INC # A4: 5,9 => UNS * INC # A4: 2,4 => UNS * INC # A5: 5,9 => UNS * INC # A5: 4 => UNS * INC # C4: 2,9 => UNS * INC # C4: 3,4,7 => UNS * INC # A9: 2,6 => UNS * INC # A9: 8 => UNS * INC # I9: 2,3 => UNS * INC # I9: 4,7,8 => UNS * INC # F8: 2,3 => UNS * INC # F8: 5 => UNS * INC # E2: 4,8 # C1: 3,7 => UNS * DIS # E2: 4,8 # B3: 3,7 => CTR => B3: 6,8,9 * INC # E2: 4,8 + B3: 6,8,9 # C3: 3,7 => UNS * INC # E2: 4,8 + B3: 6,8,9 # C1: 3,7 => UNS * INC # E2: 4,8 + B3: 6,8,9 # C3: 3,7 => UNS * INC # E2: 4,8 + B3: 6,8,9 # B3: 6,9 => UNS * INC # E2: 4,8 + B3: 6,8,9 # C3: 6,9 => UNS * INC # E2: 4,8 + B3: 6,8,9 # E3: 4,8 => UNS * PRF # E2: 4,8 + B3: 6,8,9 # E3: 3,7 => SOL * STA # E2: 4,8 + B3: 6,8,9 + E3: 3,7 * CNT 29 HDP CHAINS / 30 HYP OPENED